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Question : Find the value of the following expression. $12\left(\sin^4 \theta+\cos^4 \theta\right)+18\left(\sin^6 \theta+\cos^6 \theta\right)+78 \sin^2 \theta \cos^2 \theta$
Option 1: 30
Option 2: 40
Option 3: 10
Option 4: 20
Correct Answer: 30
Solution : $12(\sin^4 \theta+\cos^4 \theta)+18(\sin^6 \theta+\cos^6 \theta)+78 \sin^2 \theta \cos^2 \theta$ $=12[(\sin^2 \theta+\cos^2\theta)^2-2\sin^2 \theta \cos^2 \theta]+18[(\sin^2 \theta+\cos^2 \theta)^3-3\sin^2 \theta \cos^2 \theta(\sin^2 \theta+\cos^2\theta)]+78 \sin^2 \theta \cos^2 \theta$ $=12[1-2\sin^2 \theta \cos^2 \theta]+18[1-3\sin^2 \theta \cos^2 \theta]+78 \sin^2 \theta \cos^2 \theta$ $= 12-24\sin^2 \theta \cos^2 \theta+18-54\sin^2 \theta \cos^2 \theta+78 \sin^2 \theta
Question : Directions: In the following question, select the related number from the given alternatives. 11 : 1210 :: 10 : ?
Option 1: 910
Option 2: 980
Option 3: 1000
Option 4: 970
Correct Answer: 1000
Solution : Given: 11 : 1210 :: 10 : ?
112 = 121 and 121 × 10 = 1210 Similarly, 102 = 100 and 100 × 10 = 1000
Hence, the third option is correct.
Question : Select the most appropriate ANTONYM to replace the underlined word in the following sentence. Darwin drew our attention to the gradual accumulation of unfavourable traits and its direct relationship with the survival of those presumed lucky species, which then serve as breeding grounds for more desirable traits.
Option 1: advantageous
Option 2: fulfilling
Option 3: steady
Option 4: negative
Correct Answer: advantageous
Solution : The correct answer is the fourth option.
The reason advantageous is the correct antonym for unfavourable is that it directly contrasts the idea of something being unfavourable or disadvantageous. Advantageous means favourable, beneficial, or providing an advantage.
The meanings of the other words are as
Question : The Revolutionary Socialist Party was established in _______.
Option 1: 1936
Option 2: 1925
Option 3: 1940
Option 4: 1929
Correct Answer: 1940
Solution : The correct answer is 1940.
The Revolutionary Socialist Party was established in 1940. It had its roots in the Bengali liberation movement and the Hindustan Socialist Republican Army. Tridib Chaudhuri was the founder of this party.
Question : Value of $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ is:
Option 1: 1
Option 2: 2
Option 3: –1
Option 4: 0
Correct Answer: 1
Solution : $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(2\cos^2\theta-1)}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta[2(1-\sin^2\theta)-1]}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(1-2\sin^2\theta)}$ $=\sec^2\theta-\tan^2\theta$ $=1$ Hence, the correct answer is 1.
Question : Divide Rs. 14136 among A, B, and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. What is the share of C?
Option 1: Rs. 3680
Option 2: Rs. 456
Option 3: Rs. 2736
Option 4: Rs. 1413
Correct Answer: Rs. 2736
Solution : Given: Divide Rs. 14136 among A, B and C such that 2 times A's share, 3 times B's share and 5 times C's share are all equal. Let A's share, B's share and C's share are $x,y,$ and $z$ respectively. According to the question,
Question : The value of $30\%$ of $680+2 \frac{3}{11}$ of $1331$ is:
Option 1: 3230
Option 2: 3229
Option 3: 3231
Option 4: 3225
Correct Answer: 3229
Solution : Given: $30\%$ of $680+2 \frac{3}{11}$ of $1331$ $= 0.3 × 680 + \frac{25}{11} × 1331$ $= 204 + 25 × 121$ $ = 204 + 3025$ $ = 3229$ Hence, the correct answer is 3229.
Question : Preet wants to use object-oriented programming language for her application. Which among the following languages should she pick?
Option 1: Either Java or Pascal
Option 2: Pascal
Option 3: BASIC
Option 4: Java
Correct Answer: Java
Solution : The correct answer is Java.
Preet wants to utilise an object-oriented programming language for her application. A method for creating software called object-oriented programming concentrates on defining and shaping named classes as entities with properties and actions. Java is a general-purpose, object-oriented programming language that
Question : Directions: In the following question, the given sentence has four parts marked P, Q, R, and S. Choose the part of the sentence with the error and select it as your answer. If there is no error, select "No Error (S)" as your answer.
(P) The conference was (Q) attended (R) by more than one hundred delegates. (S) No Error
Option 3: 3
Option 4: 4
Correct Answer: 4
Since the sentence is grammatically accurate and doesn't need any changes. The sentence conveys the idea that there were over a hundred representatives present at the conference.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
(The meeting adjourned abruptly) by the chairperson after about an hour of intense deliberation.
(1) The meeting was adjourned abruptly
(2) The meeting was abruptly adjourned
(3)The meeting was adjourned abrupt
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
Explanation: The sentence is in the passive voice,(the voice in which the object experiences an action rather than the person that acts).
The structure for a passive sentence is: "Object + form of the be verb (in
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